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Do school inputs matter? Regression analysis of Michigan Assessment Survey Program data (1971) shows inputs are productive, but only under our new criteria. Many previous economic studies have concluded that school inputs do not matter because mean school output is often uncorrelated with input variations. But if every student's performance matters to a school, then productive inputs affect the entire distribution of student performances. If that distribution can be characterized by its mean and variance, then inputs are productive if either moment is affected. One cannot, however, tell how much these distributional effects depend on technology and how much on tastes of school authorities
Brown et al. (Sun,) studied this question.